Consider the two curves $C_1: y^2=4 x, C_2: x^2+y^2-6 x+1=0$. Then,

Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these reactions as given in column...

Match the transformations in column I with appropriate options in column II

The number of hexagonal faces that are present in a truncated octahedron is

In 1 L saturated solution of $\mathrm{AgCl}\left[\mathrm{K}_{\mathrm{sp}}(\mathrm{AgCl})=1.6 \times 10^{-10}\right], 0.1 \mathrm{~mol}$ of $\mathrm{CuCl}\left[\mathrm{K}_{\mathrm{sp}}(\mathrm{CuCl})=1.0 \times 10^{-6}\right]$ is added. The resultant concentration...

Let $\mathrm{g}(\mathrm{x})=\frac{(\mathrm{x}-1)^{\mathrm{n}}}{\log \cos ^{\mathrm{m}}(\mathrm{x}-1)} ; 0<\mathrm{x}<2, \mathrm{~m}$ and n are integers, $\mathrm{m} \neq 0, \mathrm{n}>0$, and let p be the left hand derivative of $|\mathrm{x}-1|$ at $x=1$. If $\lim _{x \rightarrow 1^{+}} g(x)=p$, then

The volume (in mL ) of $0.1 \mathrm{M} \mathrm{AgNO}_3$ required for complete precipitation of chloride ions present in 30 mL...

Among the following, the number of compounds than can react with $\mathrm{PCl}_5$ to give $\mathrm{POCl}_3$ is $...

The total number of contributing structure showing hyperconjugation (involving $\mathrm{C}-\mathrm{H}$ bonds) for the following carbocation is

The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compound is

Let $f: R \rightarrow R$ be a continuous function which satisfies $f(x)=\int_0^x f(t) d t$. Then the value of $...

If $I_n=\int_{-\pi}^\pi \frac{\sin n x}{\left(1+\pi^x\right) \sin x} d x, n=0,1,2, \ldots$, then

An ellipse intersects the hyperbola $2 x^2-2 y^2=1$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the...

For function $f(x)=x \cos \frac{1}{x}, x \geq 1$,

The tangent PT and the normal PN to the parabola $y^2=4 a x$ at a point $P$ on it meet...

Steel wire of lenght ' L ' at $40^{\circ} \mathrm{C}$ is suspended from the ceiling and then a mass '...

If the sum of first $n$ terms of an A.P. is $\mathrm{cn}^2$, then the sum of squares of these $n$...

Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting...